Performance of vehicles

1. Performance of Automobile
By
Mr. G.N. Samleti

2. Power for propulsion
• The motion of a vehicle moving on a road is resisted by air resistance
and road resistance.
• In addition to these two resistance, vehicle has to overcome Grade
resistance when it moves on a gradient, because the weight if the
vehicle is to be lifted through a vertical distance.
• Hence the power required to propel a vehicle is proportional to the
total resistance to its motion and the speed.

3. Let, Pv = power required by the vehicle.
Pe = engine b.p. required.
V = speed of the vehicle in km/hr
ηt = transmission efficiency or drive line efficiency.
R= total resistance in N. 𝑅 = 𝑅𝑎 + 𝑅𝑟 when vehicle moves along a level
road. 𝑅 = 𝑅𝑎 + 𝑅𝑟 + 𝑅𝑔 𝑤ℎ𝑒𝑛 𝑎 𝑣𝑒ℎ𝑖𝑐𝑙𝑒 𝑚𝑜𝑣𝑒𝑠 𝑢𝑝 𝑎 𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡.
Ra = air resistance in N.
Rr = rolling resistance in N.
Rg = grade resistance in N.

4. Power required for propel the vehicle is given as follow,
𝑃𝑣 =
𝑅𝑉
1000
1000
60 × 60
=
𝑅𝑉
3600
𝐾𝑊.
The engine power required will take into account the losses in
transmission.
Hence, 𝑃𝑒 =
𝑃𝑣
𝜂𝑡
=
𝑅𝑉
3600𝜂𝑡
, KW

5. Air Resistance
This is the resistance offered by air to
the movement of the vehicle.
The air resistance has an influence on the
performance, ride and stability of the
vehicle and depends upon the size and
shape of the body of the vehicle, its
speed and wind velocity.
The last term should be taken into
account when mentioned and neglected
otherwise.
Hence in general,
Air resistance 𝑅𝑎 = 𝐾𝑎𝐴𝑉2
𝐾𝑎=0.023 for streamlined car
= 0.031 for average cars
= 0.045 for trucks and lorries.

6. Rolling Resistance
The magnitude of rolling resistance mainly depends on
• The nature of road surface.
• The type of tyre viz. pneumatic or solid rubber tyre.
• The weight of the vehicle.
• The speed of the vehicle.
The rolling resistance is expressed as
𝑹𝒓 = 𝑲𝑾
Where, K = Constant or rolling resistance
K = 0.0059 for good roads, K= 0.18 for loose sand road,
K= 0.015 a representative value for undefined road.
W = Weight of the vehicle, N
A more widely used expression is 𝑹𝒓 = 𝒂 + 𝒃𝑽 𝑾,
Where, V = Speed of vehicle, km/hr and Mean values a and b are 0.015 and 0.00016
respectively.

7. Grade Resistance

8. Traction and Tractive effort.
Engine Power 𝑃𝑒 =
2𝜋𝑁𝑇𝐸
60000
Engine torque 𝑇𝐸 =
60000𝑃𝑒
2𝜋𝑁
, 𝑁. 𝑚
Torque at driving wheels 𝑇𝑤 = 𝐺𝜂𝑡𝑇𝐸
Tractive effort F =
𝑇𝑤
𝑟
∴ 𝐹 =
𝐺𝜂𝑡𝑇𝐸
𝑟
Where, 𝑇𝐸= mean engine torque.
𝜂𝑡= overall transmission efficiency.
G= overall gear ratio.,
r = radius of tyre,m.,
N= r.p.m of crankshaft.